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Nguyễn was born in the Viet Yen district of the province of Bac Giang in French Indochina, north of Hanoi. When he was 5 years old, his father, Nguyen Van Bay (Chairman of the Viet Minh in the district) and his uncle (also a member of the Viet Minh), were killed by the French. Fearing further trouble with the French, his mother relocated the family, which led to him spending the rest of his childhood near Chu air base, which kindled an interest in aircraft.

He attended Ngo Si Lien school in Bac Giang[1] and upon completion of his schooling, enlisted in the Quan Chung Khong Quan (Vietnamese People's Air Force, VPAF) in 1961 and underwent his initial training at Cat Bi Airbase in Haiphong. Nguyễn subsequently spent four years undergoing pilot training in the Soviet Union at the Bataysk and KrasnodarSoviet Air Force bases. Of the 120 trainees dispatched in Nguyễn's draft to the Soviet Union, he was one of seven who graduated as a MiG-17 pilot.

After a brief spell back in North Vietnam serving with the 921st Sao Do (Red Star) Fighter Regiment, he returned to the Soviet Union and underwent conversion training to the MiG-21 in a two-seat Mig-21U, before returning to the 921st Fighter Regiment in June 1965.[1] He began operational flying in December 1965.[1]

Flying a MIG-21PF, Nguyễn normally served as a wingman. He scored all his victories using the heat-seeking R-3S Atoll missile.

In 1969, Nguyễn was awarded a Huy Hiew medal for each of his nine claimed kills. The end of Operation Rolling Thunder on 31 October 1968 removed him from the opportunity for further air combat. In that year, Nguyễn was transferred from operational duties so that his valuable combat experience could be put to use in training new pilots. Among the pilots he trained was Nguyen Duc Soat.

After the war, Nguyễn remained with the Vietnamese National Air Force, retiring with the rank of Chief Inspector in 2002 after declining health.[1]

Nine air-to-air combat kills of United States aircraft were credited to him during the Vietnam War. Of these, seven have currently been acknowledged by the United States Air Force. While sometimes U.S. forces may have attributed aircraft losses to surface-to-air missiles, since it was considered "less embarrassing",[3] in fact there was often doubt about cause of the loss. Coc also claimed an F-4 Phantom and F-105 Thunderchief in November and 17 December 1967 but there are no corresponding American losses.

The following kills, while flying the MiG-21, have been credited to Van Coc by the VPAF (aka NVAF):[4][5]

30 April 1967: USAF F-105D piloted by Robert A. Abbott of the USAF 355th TFW.[6][7] This was his first air victory and occurred while he was acting as a wingman to Nguyen Ngoc Do, who also downed an aircraft.

23 August 1967: USAF F-4D (serial number 66-0238) of Major Charles R. Tyler (pilot) and Captain R. N. Sittner (WSO) of the 555th Tactical Fighter Squadron. Tyler was captured and Sittner was killed.[6][7]

7 May 1968: On the afternoon of 7 May 1968, three flights of MiG-21 fighters from the VPAF 921st Regiment were flying towards Tho Xuan Air Base, as part of redeployment in response to the U.S. bombing halt above the 19th Parallel. The flights were led by Dang Ngoc Ngu, Nguyen Van Minh and Nguyen Van Coc.[8] Due to the lack of coordination between the different sections of the VPAF 921st Fighter Regiment and the ground-based air-defense forces, the MiG-21 flights were mistakenly identified as U.S. fighter-bombers and were fired upon by North Vietnamese anti-aircraft artillery.[9] Moments later, Ngu also mistook an escorting flight of MiG-21 fighters flown by Nguyen Dang Kinh and Nguyen Van Lung for U.S. fighters. He dropped his fuel tanks to prepare for an attack which was promptly aborted when he realized they were North Vietnamese.[9]

Later, Ngu and Coc arrived over the skies of Do Luong, north-east of Vinh, and they made three circuits over the area when they were told that enemy aircraft were detected coming from the sea; these were real U.S. fighters.[9] The U.S. flight detected were a formation of five F-4B Phantom II from Fighter Squadron 92 (VF-92), USS Enterprise, led by Lieutenant Commander Ejnar S. Christensen.[10] Over North Vietnamese airspace, a U.S. Navy EKA-3Aelectronic warfare aircraft tried to jam North Vietnamese communications but failed, and Nhu’s flight of MiG-21 fighters was guided towards their target by ground controllers.[11]

While trying to engage the VPAF MiGs, the F-4B formation became separated due to confusion in radar control.[11] In the ensuing dogfight, two AIM-7 missiles were fired by the U.S. Navy fighters but missed.[10] Ngu then noticed two F-4B Phantoms about 5 kilometers (3.1 mi) to starboard, but could not get into a suitable firing position. Coc was right behind Ngu at the time, but he wanted to disengage from the fight as his aircraft was running low on fuel. However, Coc quickly changed his mind after he spotted an F-4B ahead of him at an altitude of 2,500 meters (8,200 ft). Coc immediately gave chase to the F-4B, which were flying out to sea, and successfully scored a hit after he fired two R-3S Atoll missiles from an altitude of 1,500 meters (4,900 ft).[9] The F-4B Phantom II burst into flames and crashed into the sea at 6:44 pm.[11]

The action gave the VPAF their first aerial victory over the airspace above the Military Zone IV of North Vietnam[9] and gave Nguyen Van Coc his seventh aerial victory.[9] The U.S. Navy confirmed that the downed F-4B had been BuNo 151485, callsign Silver Kite 210, of VF-92 launched from Enterprise.[9][10] The pilot of BuNo 151485, Lieutenant Commander Ejnar S. Christenson, and his Radar Intercept Officer, Lieutenant (jg) Worth A. Kramer ejected safely from their aircraft before impact and were recovered a short time later.[7][10][12][13]